More from this section [Book
Reviews] . . .
What a pity that this remarkable book has been so
misleadingly presented. According to the blurb, it uncovers "a new
law of nature" that applies to subjects as diverse as the "behaviour
of forest fires, the extinction of species, the pattern of
earthquakes, the rise and fall of financial markets, the flow of
traffic, the growth of cities, the outbreak of wars and even trends
in fashion, music and art". The new law is "unifying science", and
will "make it easier for us to manage and control the future".
This kind of language may bolster sales, but it will lead
thinking people to dismiss Mark Buchanan as a charlatan. It recalls
the worst pretensions of Marxism, such as Engels's attempt to
construct a "dialectic of nature" to complement the dialectic of
history. Attempts to unify the whole of human knowledge under a
single rubric are now terminally unfashionable, and any endeavour to
"make it easier for us to manage and control the future" is regarded
with peculiar suspicion.
It would be a great shame if
Ubiquity were lumped together with Marxism and other
discredited grand narratives. As a matter of fact, Buchanan's
purpose is diametrically opposed to that of previous
system-builders. The "new law of nature" described in
Ubiquity
is not a law of nature in the traditional sense at all. It is
not an attempt to explain facts in the manner of Newton, by relating
them back to deep underlying causes. Rather, it is the admission
that, for a wide variety of phenomena, there are no deep underlying
causes, just an accumulation of tiny accidents. This is a radically
new kind of physics, and it suggests a new approach to the study of
society. The example of Newtonian physics inspired such thinkers as
Marx to seek out the underlying law of historical change; the new
science suggests that such a law does not exist. A postmodern
physics has inspired a postmodern history.
Ubiquity
is not an original work of science: it is, rather, an attempt to
summarise and bring together the work of scientists in many
different fields. Buchanan's gift is for synthesis and lucid
exposition. His background is in science journalism, and he has a
journalist's feel for the intellectual limitations of his
readership. The maths is applied with restraint, and is supplemented
with concrete illustrations wherever possible. My own career in
science terminated ingloriously with a single GCSE in chemistry, yet
I found
Ubiquity fell (just) within my grasp. Nor did I
suspect - as I often do when reading popular science - that this
feeling of understanding was merely a gratifying illusion spun by
artful prose. The core ideas in
Ubiquity really are very
simple - that is their beauty. It is curious that the progress of
science is not always in the direction of ever greater complexity;
simplicity is often the mark of an intellectual breakthrough.
All the phenomena discussed here obey a certain mathematical
formula known as a power law. As they increase in scale, so they
decrease in frequency. When the size of an earthquake doubles, it
becomes four times as rare. When the size of a stock-market
fluctuation doubles, it becomes 16 times as rare. The exact fraction
does not matter; it is the general law that counts. What this law
indicates, translated into English, is that there is no such thing
as an average size for an earthquake or a stock-market fluctuation.
There is no median point around which they all cluster.
Certain phenomena - human height, intelligence - do cluster
around a central point. Plotted on a graph, they form the notorious
bell curve. But imagine for a moment, Buchanan says, that human
height obeyed a "power law" instead. What this would mean, in
practice, is that there would be no possible way of predicting the
height of the next person you bumped into. You might crush her under
your foot or, alternatively, she might crush you under her foot. And
whatever size you happened to be, the situation would be the same.
Whether you were as tall as a mountain or as small as an ant, the
human landscape would look roughly the same. It would be, in the
jargon, "scale invariant" - identical on every possible scale of
magnification. This is precisely how the landscape of earthquakes,
stock-market crashes, forest fires and wars looks. There is, in the
strictest sense, no such thing as a typical earthquake or a typical
war.
What does all this prove? So far, it looks like nothing
more than a curious but idle observation. It is all very well to
gesture to these mysterious correspondences; the important thing is
to explain them. This is what Buchanan goes on to do. Scale
invariance is, for him, no more than a symptom pointing to a common
underlying pattern of organisation. Only this common underlying
pattern does not correspond to any "law of nature". This marks a
crucial departure from traditional physics. The timeless equations
of Newton or Einstein are of no use in trying to understand
phenomena such as earthquakes or forest fires, in which accident
plays a central role. The best way to understand them is to
construct a "game of chance", combining elements of randomness with
elements of regularity. It functions as a stylised model of the real
situation, bringing out its central features and explaining its
behaviour. Such games are, needless to say, played on computers.
Indeed, this whole area of science is unthinkable without the
computer.
The game that Buchanan comes back to again and
again - which functions as an organising metaphor for his thought -
is the "sand-pile game". Devised by the physicists Bak, Tang and
Weisenfeld in 1987, the game involves sprinkling grains of sand, one
at a time, on to a table top. The grains soon form piles, which grow
steeper and steeper until an errant grain triggers an avalanche and
the pile flattens out again. They then asked a simple question: what
is the average size of an avalanche? But however many times they ran
the game through the computer, they could arrive at no answer. A
falling grain might dislodge anything from one to a million other
grains. The distribution of avalanches obeyed our old friend the
power law: double the number of grains involved, and the avalanche
becomes slightly more than twice as unlikely.
What is it
about grains of sand on a table that produces this curious
statistical result? The precise physical properties of sand are
irrelevant. The computer simulation captures what one might call the
logic of the situation, while discarding all that is accidental to
it. This logic turns out to be identical in all the phenomena
discussed by Buchanan. The composition of the individual items does
not matter at all; they might be grains of sand, trees in a forest,
atoms in a magnet or traders on the stock-market floor. All that
matters, for the purpose of the game, is that they are organised
into what is known as the "critical state". This is what makes the
application of the new physics to human society more than merely
metaphorical. There is a sense in which grains of sand and human
beings really are behaving according to similar laws. The historic
division between the social and the natural sciences may at last be
coming to an end.
One of the most important conclusions of
Ubiquity is that, for systems organised into the critical
state, there is no difference in principle between the small and the
large. There is no special class of "great events" that requires
special explanation. "Large events are just magnified copies of
smaller ones, and arise from the same kinds of causes." This is
important, because it runs against our natural inclination to
believe that great events must have great causes. Geologists have
sought out the causes of great earthquakes, and economists have
sought out the causes of great crashes, as though these could
somehow be set apart from the tiny tremors that daily afflict the
earth's crust and the financial markets. Buchanan suggests that they
are, in fact, nothing more than larger versions of these tiny
tremors, and require no special analysis.
Applied to
history, this theory suggests that great wars and revolutions demand
no explanation beyond a narration of the precise chain of events
that compose them. In the sand pile, it is impossible to specify the
cause of a huge avalanche other than by tracing its exact progress
right back to the original grain that triggered it all off. There
are no "laws of avalanches" distinct from the laws governing the
movement of the individual grains. And any grain - the unfortunate
Gavrilo Princip in Sarajevo springs to mind here - can, if it falls
at the right time and place, start an avalanche. The only way to
understand the history of the sand pile is to recount it;
old-fashioned narrative history turns out to be the most scientific
of all.
The vision of history that emerges from
Ubiquity
is tragic. It is the vision of the
Iliad. History stands
permanently poised on the brink of catastrophe; the abduction of one
woman can lead to the destruction of cities. Instability is an
inalienable feature of human life. We flatter ourselves that we have
overcome it through the development of rules and institutions, not
realising that those very rules and institutions are equally subject
to its depredations. The very existence of the human race is
precarious; the tiniest fluctuation at some random point in the
ecosystem could unleash on us an avalanche of extinctions.
The predicament of the individual is equally tragic. Human
society is configured in such a way that each individual action may
have consequences that are vast but totally unforeseeable. Each of
us stands, potentially, at the pivot of world history; anyone can be
the grain that brings the pile tumbling down. We are thus burdened
with an awesome responsibility, yet at the same time denied any
means of knowing how to discharge it. What practical consequences
follow from this? Is there an "ethics of the sand pile"? This
question awaits another book.
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